Neutralising monoclonal antibodies can prevent and treat COVID-19 if administered early after infection with sensitive SARS-CoV-2 variants. Despite containing reasonable levels of neutralising antibodies (1098-1593 IU/mL), hyperimmune intravenous immunoglobulin (hIVIG) failed to mitigate severe COVID-19 in a recent trial in hospitalised patients (NCT04546581). We probed potential reasons for this discrepancy. Based on previous work on human influenza A, we hypothesised that higher baseline spike (S) antibody-specific Fc gamma receptor (FcγR) engagement may promote inflammation and lead to poorer clinical outcomes. We focused on S-specific FcγRIIIa binding activity, a surrogate of antibody-dependent cellular cytotoxicity (ADCC), in pre-treatment serum samples from 481 subjects (n = 231 placebo vs. n = 250 hIVIG). We found that elevated levels of FcγRIIIa engagement by baseline S-specific antibody were associated with better outcomes in patients hospitalised with COVID-19, which was the opposite of our primary hypothesis. Associations between better clinical outcome and high baseline ADCC activity were consistent in both the hIVIG- and placebo-treated groups. Higher nucleocapsid (N) antibody-mediated FcγR engagement and surrogate neutralising activity in pre-treatment sera were also modestly associated with improved clinical outcomes in hospitalised COVID-19 patients. The high prevalence of pre-therapy FcγR binding antibody at hospitalisation, along with the rapid production of these antibodies in placebo-treated subjects, may dilute any potential benefit from hIVIG therapy in patients hospitalised with COVID-19. This work could help guide development of more strategic and targeted treatment of severe SARS-CoV-2 infection with antibody-based therapeutics.